Mortality multipliers for exceeding ward or ITU capacity in the COVID-19 pandemic.

On Friday the 29th January 2021, the report “Direct and Indirect Impacts of COVID-19 on Excess Deaths and Morbidity: November 2020 Update” by the Department of Health and Social Care, the Office for national Statistics, the Government Actuaries department and the Home Office was released (1).

It was a view, from the 17th December 2020, as to the possible impacts of COVID-19 pandemic. It concluded that there could be an additional 97,000 direct excess deaths from COVID-19 over the winter and an additional 76,000 excess deaths from other causes accelerated as a result of the disruption to NHS services caused by the pandemic. In addition, another 55,000 deaths arising from changes to emergency care and the disruption of adult social care would be expected.

Crystallise supported the section of this report on excess deaths arising from the breaching of NHS capacity, and the section on long-COVID. This post unpacks the approach that was taken to estimating the deaths arising from exceeded capacity. The full paper is available as a preprint on MedRxiv here (2).


We worked with a small team of two actuaries, Stuart McDonald and Steve Bale, an epidemiologist Michiel Luteijn, and with advice from an NHS critical care consultant Dr Rahul Sarkar. Our task was to  estimate the number of deaths that would occur if intensive care or general hospital ward capacity was breached. Our role was to estimate how mortality would scale up for those who were refused an intensive treatment unit (ITU) or general ward bed because of an exceedance of capacity.

At first sight, this seems an un-modellable problem. There are no randomized controlled trials of providing critical or hospital care when it is needed as it would be quite unethical to do so, and no previous experience of a large-scale event like the COVID-19 pandemic where NHS care was overwhelmed.

Estimating a scalar applicable across all NHS care would be impossible, and so the approach taken was to break the problem down using the pathways of care for COVID-19 patients who required hospital care.

We began with an outline of the different pathways of care that could be experienced by someone admitted with COVID-19, and this is shown in the figure below.



“O2>35%/HFO” indicates a group of people who require unusually large amounts of oxygen to keep there blood oxygen levels at a safe enough level. “NIV/CPAP” refers to patients on ITU who require non-invasive ventilation such as continuous positive airways pressure (CPAP). “IMV” refers to those who require treatment on a mechanical ventilator, and “ECMO” refers to those who required artificial oxygenation of the blood using ‘extra-corporeal membrane oxygenation’.

We then used data on those hospitalized in the pandemic in the UK to estimate the numbers of people that fall into each of these ‘compartments’ of care and the mortality rates experienced in each of those compartments. The figure below shows the compartments in the spreadsheet populated with the estimates.





“Ceiling” refers to those people who are simply too unfit to be able to survive more aggressive forms of treatment and so may die from COVID-19 in this compartment.

We then got to the hard bit – estimating how the mortality changes in each of these compartments should the category of care be taken away. For some groups, such as those needing mechanical ventilation, the estimate of near 100% fatality is quite reliable. However, some compartments of care required a certain amount of judgement and remain uncertain. To reduce the likelihood of significant error in these judgments, two clinicians were involved, a GP and a critical care consultant.

By breaking the problem down into its component parts, we can be more confident about the estimates than we otherwise would be. The scale of the judgements are likely to be fairly sound (none, small minority, minority, evens, majority, large majority, all), and the error in those estimates is restricted to that compartment only. Assuming there is no systematic bias in those making the judgements, you would expect the errors across a number of compartments to be lower than in a single compartment as the errors will occur in each direction with equal probability.


In general, the deaths will occur in those compartments that are ‘ceilings of care’, either compartments where the occupants are too unfit to survive a riskier category of intervention, or the natural ceiling of IMV or ECMO. For these categories, a failure to provide the treatment will result in death in the great majority of cases. There are risks associated with these categories of treatment and they would not usually be deployed unless they were not felt to be lifesaving.

For example, for those needing supportive care or high-flow oxygen only on ITU, they will have a low mortality rate, otherwise they would have been escalated to CPAP or IMV, hence the choice of 1% mortality. If the true value is as much as 5%, the difference is only 4%, and then only 48% of this error will be transmitted – about 2%.  Some will still die in this compartment from sudden events like a heart attack or stroke, but rarely from respiratory failure. Anyone that deteriorated would have been escalated to one of the higher risk intervention groups like CPAP before death occurs. The excess death from exceeding capacity would therefore primarily appear in one of these ‘ceiling’ compartments. On the whole, taking away this care is likely to increase mortality, but not by much, as they are receiving care that could be provided on a ward. However, the staff ratios would be less on the ward and less they are less well geared up for the sickest of patients, so the risk is doubled from 1% to 2%.

Taking the compartment of those who have non-invasive ventilation / CPAP as a ceiling of care, we have observational data that says about 83% of this group die. Even though this parameter is data rather than judgement driven, it will still have error, but we can be reasonably confident that its scale will be similar.

Full details on each compartment with the associated assumptions can be found in the preprint online (2).


  1. DHSC, ONS, GAD, Home Office. Direct and Indirect Impacts of COVID-19 on Excess Deaths and Morbidity: November 2020 Update. 2020.
  2. McDonald S, Martin C, Bale S, Luteijn M, Sarkar R. Construction of a demand and capacity model for intensive care and hospital ward beds, and mortality from COVID-19. MedRxiv [Internet]. 2021; Available from:
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